Category: Algebra

Question Number 156180 by SANOGO last updated on 08/Oct/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 156172 by MathSh last updated on 08/Oct/21 Commented by Rasheed.Sindhi last updated on 09/Oct/21 $$\mathrm{Infinitely}\mathrm{many}\mathrm{sets}.$$ Commented by MathSh last updated on…

Question Number 156164 by MathSh last updated on 08/Oct/21 Answered by ghimisi last updated on 09/Oct/21 $$\mid x\mid =\frac{1}{2}\mid x+y+x-y\mid ⩽\frac{1}{2}\mid x+y\mid +\frac{1}{2}\mid y-x\mid \left(1\right)$$$$\mid y\mid =\frac{1}{2}\mid y+x+y-x\mid ⩽\frac{1}{2}\mid x+y\mid +\frac{1}{2}\mid y-x\mid \mid \left(2\right)$$$$\mid 3x+2y\mid =\mid 4x+3y-(x+y)\mid ⩽\mid 4x+3y\mid +\mid x+y\mid \left(3\right)$$$$\left(1\right)+\left(2\right)+\left(3\right)\Rightarrow$$$$\mid{x}\mid+\mid{y}\mid+\mid\mathrm{3}{x}+\mathrm{2}{y}\mid\leqslant\mid\mathrm{4}{x}+\mathrm{3}{y}\mid+\mathrm{2}\mid{x}+{y}\mid+\mid{y}−{x}\mid…

Question Number 156152 by amin96 last updated on 08/Oct/21 $$\{\begin{array}{l}\mathbf{a}+\mathbf{b}+\mathbf{c}=1\\ {\mathbf{a}}^2+{\mathbf{b}}^2+{\mathbf{c}}^2=2\\ {\mathbf{a}}^3+{\mathbf{b}}^3+{\mathbf{c}}^3=3\end{array}$$$${\mathbf{a}}^6+{\mathbf{b}}^6+{\mathbf{c}}^6=?$$ Commented by…

Question Number 25074 by Mr easy last updated on 03/Dec/17 Commented by moxhix last updated on 03/Dec/17 $$(x-a)(x-b)(x-c)(x-d)=0$$$$x^4-(a+b+c+d)x^3+(ab+bc+cd+da)x^2-(abc+bcd+cda+dab)x+abcd=0$$$$$$\{\begin{array}{l}a+b+c+d=0\\ ab+bc+cd+da=0\\ abc+bcd+cda+dab=k\\ abcd=-15\end{array}$$…